In the Summer of 1995, all of America was trying to solve the mystery of who shot Mr. Burns. Then they found out it was the baby. Many were shocked that The Simpsons made Maggie the one who pulled the trigger, but if you go back through the first part of "Who Shot Mr. Burns", she's really the only viable suspect.
A two-part story told across The Simpsons season 6 finale and season 7 premiere, "Who Shot Mr. Burns" stands as an emblem of the show at its peak. It saw The Simpsons tackle various mystery genre tropes ("Part 2" riffs on Twin Peaks' Black Lodge visions brilliantly), tell a story that takes into account the entire town, and, most excitingly of all, actually create a mystery that's solvable. Nobody actually did crack the case - only one entry in the phone-in contest was correct and that person was never found - but if you go back through the first part of "Who Shot Mr. Burns", all the evidence that it's Maggie is there.
So yes, at the very end of "Who Shot Mr. Burns", it's revealed Maggie shot the 104-year-old by accident (or was it?) after he tried to steal her lollipop and his gun fell out of his holster and into her hands. This is, in part, a result of the writers wanting to avoid having to deal with the ramifications of an adult being the shooter - and thus having to write them out - although it gelled well with her violent streak in "Itchy & Scratchy & Marge" as well as history with Burns' bear Bobo. There's also copious teases in the second part - such as Simpsons DNA - which further point towards Maggie. That's all circumstantial, of course, and unnecessary.
If you were watching The Simpsons casually and felt it came out of left-field - season 7's "The Simpsons 138th Episode Spectacular", which aired just a couple of months later, even winked towards that - here's how you could crack it (hat-tip to YouTuber Eddache and Reddit).
- This Page: Maggie Is The Most Fitting Subject After Who Shot Mr. Burns - Part 1
- Page 2: The Sundial & Candy Clues In Who Shot Mr. Burns
Why Smithers Couldn't Have Shot Mr. Burns
Going into "Who Shot Mr. Burns - Part 2", the obvious suspect is Waylon Smithers. The first part is very much his decent as he tries to stop Mr. Burns' sun-blocking plan, and indeed that's who the Springfield police gravitate towards: he's the go-to suspect when Lou questions Maggie and Santa's Little Helper, and even Smithers himself thinks he did it.
He's ultimately proven innocent by Sideshow Mel. Krusty's intelligent-beyond-his-bone sidekick figures out that Smithers would have been home watching Pardon My Zinger on Comedy Central at the time of the shooting, an extension of a jab at Comedy Central from the previous episode. And all the information that Mel used was there in "Who Shot Mr. Burns - Part 1".
Smithers states in the town meeting he never misses Pardon My Zinger, while a TV screen in Moe's earlier in the episode showed an advert for the show with a prominently displayed 3 pm air time. This is the same time Burns blocked out the sun and he's subsequently shot, which clearly exonerates Smithers.
Maggie Fits All The Mr. Burns Shooter Descriptions
Once Smithers is discounted, The Simpsons' big mystery seems a lot trickier. Everybody in Springfield - except Marge and Jimbo who are seen around the time of the shooting - is a suspect, with a suitable motive and lack of alibi. To cut it down, it's worth looking at what little is known of the struggle that led to the shooting: Burns knows the shooter, recognizing them with an upbeat "oh, it's you"; Burns is likely shot with his own gun as it's missing from its holster after being shot; and the shooting takes place in the carpark behind Town Hall, a location provided by Burns' Springfield map earlier in the episode.
Recognizing the shooter rules out Homer (and, following the chocolate box featuring the Simpsons family, can still include any of the children), while the weapon means the majority of those shown with their own, different weapon - Abe, Moe, Barney, Skinner - are also discounted. The carpark isn't as strong evidence as it's easily accessible by anybody in the meeting, but the only two characters confirmed in the location are Maggie and Santa's Little Helper.
Based on the context of the situation that The Simpsons season 6 finale constructs, Maggie is the one true logical suspect. And more overt evidence backs that up further.